The U.S. began the year with an awkwardly arranged deal that raised taxes. I hope it doesn’t end the year without a deal to limit spending.

The U.K. may have embraced austerity too soon, but the U.S. is far enough along in its recovery that it can begin balancing its books. An impressive new series of papers has estimated the impact of public spending on jobs during the recession, and concluded that we can make moderate budget cuts without sending the economy into a tailspin.

In the long run, the labor market will be able to adjust to less government spending, but in the short run, reductions in spending will mean fewer jobs. Last week’s figures from the Bureau of Labor Statistics showed that the unemployment rate was steady at 7.8 percent and that the U.S. private sector added 1.9 million jobs last year. Those numbers are healthy enough for us to contemplate cutting spending now. Before deciding, however, we should understand what cuts will do to employment in the short run.

How do economists estimate the impact of changes in government spending on jobs and joblessness? There is a long tradition of predicting how government spending will affect overall employment. One approach is to focus on the time pattern of jobs and spending at the national level. It is pretty hard to get much that is definitive, however, because the U.S. economy as a whole has so many moving parts.

Therefore, smart researchers have increasingly turned to state-by-state comparisons. Some of our best estimates of the impact of spending on employment come from recent studies comparing the experiences of various states under the American Recovery and Reinvestment Act of 2009 — the federal stimulus program. These findings help us assess how quickly we can cut spending. First, however, researchers have to deal with a big obstacle in looking at this data. What if federal aid disproportionately went to needier states? What if it favored states that were recovering less quickly? In that case, the aid would look as if it wasn’t doing much good, even if it was stopping a bad situation from getting much worse. Data mavens have long used “instrumental variables” to deal with this kind of challenge. If you are trying to understand the spending-to-jobs link, this method requires a third variable that randomly causes spending to rise in some places but not in others, and that doesn’t have any direct effect on employment.

Luckily for researchers, the stimulus package didn’t help every state equally, and some reasons for the different spending levels look pretty random. Lower-density states got more money for transportation-related projects, because spending followed standards that base highway trust payments on total highway and vehicle miles traveled. States that have more senior congressional delegations also received more funding.

So let’s see how this statistical wizardry changes the results. Economist Bruce Sacerdote, together with his Dartmouth College colleague James Feyrer, first looked at whether states that got more money in the Recovery Act saw an increase in employment. They estimate that there was an extra job for every $107,000 in extra stimulus spending, but that figure is potentially compromised by the more-money-to-troubled-places problem.

Feyrer and Sacerdote then factor in the seniority of a state’s congressional delegation. (The most senior congressman is ranked first and the least senior congressman is ranked 435th.) They found that as the average rank of a state’s House delegation increased by 50, the state received $165 more per capita in the stimulus package. By comparing states with more or fewer senior delegations, and hence bigger or smaller stimulus packages, economists can better estimate the effect that spending has on jobs.

Using this seniority-based formula, the researchers estimated that a job costs about $50,000 a year.

They found an even stronger connection between spending and employment when they looked at month-to-month changes in stimulus spending and state-level employment. (In this case, they had no special third variable, but they could control for the average level of employment in the state over the same time period.)

The data showed that an extra $100,000 in a month creates slightly more than 3.2 jobs, but “this indicates a cost of about $300,000 per job over the course of a year for this subset of spending.” They also looked at whether job growth persists after the stimulus and found little evidence for that.

Some categories of stimulus spending were more effective than others in creating jobs. Funding for transportation and aid supporting those with low incomes had a relatively large effect on jobs. But providing money for local governments, especially through education support, does little for state employment. (Maybe the states that received less money didn’t actually fire their teachers, or maybe the dismissed teachers found work elsewhere.)

Daniel Wilson of the Federal Reserve Bank of San Francisco similarly concludes that transportation spending seems to do as much for jobs as anything else during a slowdown — that the stimulus spending “in its first year yielded about eight jobs per million dollars spent, or $125,000 per job.”

There is something of a consensus that federal dollars do more to affect jobs during the depths of a recession, which is why the recovery makes it easier for us to contemplate spending cuts. If we start with Wilson’s $125,000-per-job number seriously, this means that reducing annual government spending by $125 billion would mean somewhat less than 1 million fewer jobs, at least in the short run. That is a considerable figure and probably more than the U.S. would feel comfortable losing right now.

If we cut only $50 billion, this should mean 400,000 fewer jobs, and possibly less if the effect of public spending on employment is weaker today than it was during the recession. That’s a serious loss, but if private-sector job creation continues at its current annual rate of 1.9 million a year, private-sector growth could offset that loss in less than three months.

The data hold out hope. It is time to start thinking beyond the present, and embrace the spending cuts that will mean a smaller debt burden for our children.

Edward Glaeser, an economics professor at Harvard University, is a Bloomberg View columnist. He is the author of “Triumph of the City.” His email address is eglaeser@harvard.edu.

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